Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits

Efficiently estimating large sets of non-commuting observables is an important subroutine for many quantum algorithms. Here we present our derandomized shallow shadow (DSS) algorithm for learning the estimated values of a set of non-commuting observables, using only short-depth rotations into each measurement basis. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of depth-$d$ measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement in comparison with state-of-the-art techniques for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems. We observe that DSS performance consistently improves as one allows deeper measurement circuits. Our work paves the way toward efficient measurement of many observables using short-depth Clifford circuits, enhancing scalability in quantum algorithm applications.